Question
Which equation matches the solution set of {5}{5}?(1 point)
Responses
x2−10=15x2−10=15
x squared minus 10 equals 15
2x−20=30 2x−20=30
2 x minus 20 equals 30
x+x−9=1+x x+x−9=1+x
x plus x minus 9 equals 1 plus x
3x5+4=7
Responses
x2−10=15x2−10=15
x squared minus 10 equals 15
2x−20=30 2x−20=30
2 x minus 20 equals 30
x+x−9=1+x x+x−9=1+x
x plus x minus 9 equals 1 plus x
3x5+4=7
Answers
GPT-4o mini
To find the equation that matches the solution set of \{5\}, we need to evaluate each given equation for the possibility of having only the solution \(x = 5\).
1. **Equation: \(x^2 - 10 = 15\)**
Rearranging gives:
\(x^2 = 25\)
\(x = 5\) or \(x = -5\)
**Solution set: \{5, -5\}** (does not match)
2. **Equation: \(2x - 20 = 30\)**
Rearranging gives:
\(2x = 50\)
\(x = 25\)
**Solution set: \{25\}** (does not match)
3. **Equation: \(x + x - 9 = 1 + x\)**
Simplifying gives:
\(2x - 9 = 1 + x\)
\(2x - x = 10\)
\(x = 10\)
**Solution set: \{10\}** (does not match)
4. **Equation: \(3x + 4 = 7\)**
Rearranging gives:
\(3x = 3\)
\(x = 1\)
**Solution set: \{1\}** (does not match)
None of the provided equations have a solution set that matches \{5\}. Therefore, please verify if all options were listed, or if there might be a mistake somewhere in the problem setup.
1. **Equation: \(x^2 - 10 = 15\)**
Rearranging gives:
\(x^2 = 25\)
\(x = 5\) or \(x = -5\)
**Solution set: \{5, -5\}** (does not match)
2. **Equation: \(2x - 20 = 30\)**
Rearranging gives:
\(2x = 50\)
\(x = 25\)
**Solution set: \{25\}** (does not match)
3. **Equation: \(x + x - 9 = 1 + x\)**
Simplifying gives:
\(2x - 9 = 1 + x\)
\(2x - x = 10\)
\(x = 10\)
**Solution set: \{10\}** (does not match)
4. **Equation: \(3x + 4 = 7\)**
Rearranging gives:
\(3x = 3\)
\(x = 1\)
**Solution set: \{1\}** (does not match)
None of the provided equations have a solution set that matches \{5\}. Therefore, please verify if all options were listed, or if there might be a mistake somewhere in the problem setup.